This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the transform coefficient squared (to within a constant factor), is equivalent to the integration of energy (in physical space) over the influence period (time scale) the series spans. Thus, a physically consistent definition of energy for the wavelet power spectrum should be the transform coefficient squared divided by the scale it associates. Such adjusted wavelet power spectrum results in a substantial improvement in the spectral estimate, allowing for a comparison of the spectral peaks across scales. The improvement is validated with an artificial time series and a real coastal sea level record. Also examined is the previous example of the wavelet analysis of the Niño-3 SST data.

[1] Patterns of ocean current variability are examined on the West Florida Shelf by a neural network analysis based on the self-organizing map (SOM), using time series of moored velocity data that span the interval October 1998-September 2001. Three characteristic spatial patterns are extracted in a 3 Â 4 SOM array: spatially coherent southeastward and northwestward flow patterns with strong currents and a transition pattern of weak currents. On the synoptic weather timescale the variations of these patterns are coherent with the local winds. On the seasonal timescale the variations of the patterns are coherent with both the local winds and complementary sea surface temperature patterns. The currents are predominantly southeastward during fall-winter months (from October to March) and northwestward during summer months (from June to September). The spatial patterns extracted by the (nonlinear) SOM method are asymmetric, a feature that is not captured by the (linear) empirical orthogonal function method. Thus we find for the synoptic weather and longer timescales that (1) southeastward currents are generally stronger than northwestward currents, (2) the coastal jet axis is located further offshore for southeastward currents than for northwestward currents, and (3) the velocity vector rotations with depth are larger in shallower water when the currents are southeastward relative to when the currents are northwestward.